The integrated rate equation for a first-orde | vedclass

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(C) For a first-order reaction,the rate of reaction is proportional to the first power of the concentration of the reactant.The differential rate equa

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$kt = 2.303 \, \log \frac{[A]_0}{[A]}$

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(C) For a first-order reaction,the rate of reaction is proportional to the first power of the concentration of the reactant.The differential rate equation is: $-\frac{d[A]}{dt} = k[A]$.Integrating this expression between the limits $t = 0$ at $[A] = [A]_0$ and $t = t$ at $[A] = [A]$,we get:$\ln \frac{[A]_0}{[A]} = kt$.Converting the natural logarithm to base $10$,we multiply by $2.303$:$2.303 \, \log \frac{[A]_0}{[A]} = kt$.Thus,the correct integrated rate equation is $kt = 2.303 \, \log \frac{[A]_0}{[A]}$.

The integrated rate equation for a first-order reaction is:

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